Graphing Tangent and Cotangent
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Transcript of Graphing Tangent and Cotangent
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Graphing Tangent and Cotangent
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Graphing Tangent Curve y = tan (x)
0
/6
/4
/3
/2
2/3
3/4
5/6
7/6
5/4
4/3
3/2
5/3
7/4
11/6
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Graphing Cotangent Curvey = cot (x)
0
/6
/4
/3
/2
2/3
3/4
5/6
7/6
5/4
4/3
3/2
5/3
7/4
11/6
2
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Using the Graphing CalculatorMode—
RadiansFunctionSequential
• Window—– X min = - – X max = 3– X scale = /6
• Window—– Y min =-3– Y max = 3– Y scale = .5
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Press Y=y1 = tan (x)
y2 = 3tan (x)
Press Graph
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Press Y=y1 = tan (x)
y2 = 4tan (x)
Press Graph
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Press Y=y1 = tan (x)
y2 = -4tan (x)
Press Graph
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Press Y=y1 = tan (x)
y2 = tan (x) +1
Press Graph
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Press Y=y1 = tan (x)
y2 = tan (x +1)
Press Graph
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Press Y=y1 = tan (x)
y2 = tan (2x)
Press Graph
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Press Y=y1 = tan (x)
y2 = tan (1/2x)
Press Graph
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Y = A tan (Bx - C) ± D
No Amplitude,
but determines two points
on the graph.
Period
|B|
Vertical Shift up/down
Horizontal ShiftLeft/Right
C B
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y = A tan (Bx – C) + D
InterceptMaximum?AsymptoteMinimum?Intercept
Unless A = Negative #InterceptMinimum?
AsymptotesMaximum?Intercept
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Press Y=y1 = 1/tan (x)
y2 = 3/tan (x)
Press Graph
y = cot (x)
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Press Y=y1 = 1/tan (x)
y2 = 4/tan (x)
Press Graph
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Press Y=y1 = 1/tan (x)
y2 = -4/tan (x)
Press Graph
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Press Y=y1 = 1/tan (x)
y2 = 1/tan (x) +1
Press Graph
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Press Y=y1 = 1/tan (x)
y2 = 1/tan (x +1)
Press Graph
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Press Y=y1 = 1/tan (x)
y2 = 1/tan (2x)
Press Graph
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Y = A cot (Bx - C) ± D
Period |B|
Vertical Shift up/down
Horizontal ShiftLeft/Right
C B
No Amplitude,
but determines two points
on the graph.
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y = A cot (Bx – C) + D
AsymptoteMaximum?InterceptMinimum?Asymptote
Unless A = Negative #AsymptoteMinimum?Intercept
Maximum?Asymptote
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Examples--y = 3tan (x + 1) -3
Amp.= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________
y = cot (x - 2) Amp.= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________
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y = cot (2x)Amp.= _______Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________
y = ½ tan (½ x) + 1 Amp.= _______
Period = _____Horizontal Phase Shift = _________Vertical Phase Shift = ________
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Graphing by Key Pointsy = 2 tan x
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/4, )
(/2, )
(3/4, )
(, )
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Graphing by Key Pointsy = -2 cot x
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/4, )
(/2, )
(3/4, )
(, )
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Graphing by Key Pointsy = tan (1/2x)
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/2, )
( , )
(3/2, )
(2, )
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Graphing by Key Pointsy = 3 cot 1/2x
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/2, )
(, )
(3/2, )
(2, )
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Graphing by Key Pointsy = 3 tan x +2
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/4 )
(/2, )
(3/4, )
(, )
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Graphing by Key Pointsy = cot x - 2
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(/4 )
(/2, )
(3/2, )
(, )
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Graphing by Key Pointsy = -tan (x + )
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(-, )(-3/4 , )
(-/2 , )
(-/4, )
(0, )
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Graphing by Key Pointsy = cot (x - /4)
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(/4 , )(/2, )
(3/4, )
(, )
(5/4, )
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Graphing by Key Pointsy = 4tan (x/2 + /2)
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(-, )(-/2 , )
(0, )
(/2, )
(, )
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Graphing by Key Pointsy = -cot x
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(0, )(1/4, )
(1/2, )
(3/4, )
(1, )
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Graphing by Key Pointsy = 2tan (x/2 - /2) -1
Amp = _________ Horizontal Shift = _______Period = _______ Vertical Shift = _________
Inc. = ________
(, )(3/2, )
(2, )
(5/2, )
(3, )